From Fluid to Braid: A Relational-Ontological Model of Value and Power, and Its Computational Horizon

We develop a formal model of how value and power circulate in relational systems, in which relations are prior to the entities they relate. A fluid-dynamical description yields one exact result---the appropriative, gradient part of value transport contributes nothing to circulation, so genuine relational value is non-possessive---but is shown to be ontologically self-undermining, since it presupposes a background and conserves what value must be free to generate. We resolve this by taking a symmetry pre-structure G as primary and letting spontaneous symmetry breaking G→ H generate the rest: the order-parameter space arises as $M=G/H$, subjects are its topological defects πₖ(G/H), the surplus of a closed cycle is the holonomy on $G/H$ (matching the Marxian circuit $M\!-\!C\!-\!M'$, with the local field value as stock), and power is its non-commutativity, which holds exactly when H is non-abelian---whence power, resonance, and generativity flow from one condition. The braid group of defect statistics is derived rather than posited. We prove that normative discriminating power requires a representation that is non-abelian yet non-universal, draw the corollary that power is ineliminable wherever there is generativity (so justice is the shaping of its geometry, not its removal), add a dynamical layer and a computational horizon, and give a falsifiable, scale-invariant operationalization with a case study in educational ethics.